Davydov-Ansatz for Landau-Zener-Stueckelberg-Majorana transitions in an environment: Tuning the survival probability via number state excitation

Abstract

We theoretically investigate transitions in a two-level system, which are induced by a sweep through an avoided crossing in the presence of coupling to a single, excited bosonic mode. This allows us to propose the initial bosonic excitation into a number state as a new possible control parameter for the survival probability at long times. The expansion of number states in terms of coherent states centered around points on a circle in phase space makes a multi-Davydov-Ansatz the method of choice to perform the required numerical calculations. It is revealed that the starting time of the transition greatly affects the final transition probabilities. In addition, we found that the mixing angle, which is tuning between the diagonal and off-diagonal coupling, is decisive for the ability to control the transition via number state excitation. For a mixing angle of π/4, we found the maximal effect of number state excitation on the transition probability.Published under license by AIP Publishing. https://doi. ARTICLEscitation.org/journal/jcp FIG. 7. Transition probabilities as a function of n: θ = 0 (blue), θ = π/4 (red), and θ = π/2 (green). APPENDIX: PROPERTIES OF THE DISPLACEMENT OPERATOR AND THE LAGUERRE POLYNOMIALSIn the following, we collect properties of the displacement operator and its action on number states that are frequently needed in

Temperature effects on singlet fission dynamics mediated by a conical intersection

“…To treat Hamiltonians with off-diagonal coupling terms, Davydov D 2 trial states of multiplicity M, which essentially sum over M copies of the corresponding single-state Davydov D 2 Ansatz, are deployed to boost simulation accuracy. A generalized multi-D 2 Ansatz of multiplicity M for the displaced number state |⃗ n⟩ = |n 1 n 2 ⋯nw⟩ used to include temperature effects reads 37,38…”

“…., N − 1. Following the suggestion of Werther et al, 37 for the Davydov-D 2 Ansatz with multiplicity M ≥ N w (w is the number of modes that may be excited), the initial conditions with the w phonon modes read…”

“…37, for N between 5 and 14 depending on various initial excitations n. In the subsequent simulations, we, thus, adopt |β l | = √ n l , the value of best performance. 37 In the present work, we monitor temperatures in the range from 0 K to 300 K (0 eV-0.0259 eV). The total phonon energy considered is, thus, within 0 eV-0.13 eV.…”

“…Werther et al have recently proposed an approach that can be efficiently employed to introduce temperature effects into the Davydov trial states. 37,38 Two alternative approaches, the sampling of P-function method 39 and the thermo-field dynamics method, [40][41][42] are numerically demanding, which makes their application to the evaluation of third-order response functions somewhat time consuming.…”

Polaron dynamics of Bloch–Zener oscillations in an extended Holstein model

“…In that respect we say that the method is numerically accurate within the theoretical model of the system. The method has been applied to a multitude of systems, including a Holstein model of polaron dynamics in the presence of external fields [54][55][56], phase transitions in the spin-boson model [57] or singlet fission model [58], a dissipative LZ model that is based on QED protocols [41,59] and other investigations in quantum optics [60,61].…”